Wavelet packets and wavelet frame packets on local fields of positive characteristic

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:395

Article

Behera, Biswaranjan¹  Jahan, Qaiser¹ 

[1] Indian Stat Inst, Theoret Stat & Math Unit, Kolkata 700108, India

关键词: Wavelet;    Multiresolution analysis;    Local field;    p-series field;    Wavelet packet;    Wavelet frame packet;   

DOI  :  10.1016/j.jmaa.2012.02.066

来源: Elsevier

【 摘 要 】

Using a prime element of a local field K of positive characteristic, the concepts of multiresolution analysis (MRA) and wavelets can be generalized to such a field. We prove a version of the splitting lemma for this setup and using this lemma we construct the wavelet packets associated with such MRAs. We show that these wavelet packets generate an orthonormal basis by translations only. We also prove an analogue of the splitting lemma for frames and construct the wavelet frame packets in this setting. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free